Calculating Time for Bolt to Fall in Elevator with Constant Acceleration

[physics kiddy]

Homework Statement

It's a question from IE Irodov's General Physics -->

An elevator car whose floor to ceiling is equal to 2.7m starts ascending with constant acceleration 1.2m/s². 2s after the start a bolt begins to fall from the ceiling of the car .Find

(a) the time after which bolt hits the floor of the elevator.

It's only the first part of the problem ...

Homework Equations

The Attempt at a Solution

After two seconds of start, the elevator catches a speed of v = 2.4 m/s ...
Then, I assumed that after t seconds the event of bolt falling on floor occurs ...

So the elevator floor covers a distance of 2.4t + 1/2at²
And the bolt covers 1/2gt²

Using some intution, I got

2.4t + 1/2at² + 1/2gt² = 2.7
Solving it, my answer comes out t = 0.5 seconds but the answer is 0.7.

Please don't solve it using relative speed of bolt with respect to elevator or any other method... just let me know what's wrong with my solution.

 

[Doc Al]

So the elevator floor covers a distance of 2.4t + 1/2at²

OK.

And the bolt covers 1/2gt²

You neglected the initial speed of the bolt. This assumes it's dropped from rest.

Correct that and you'll get the right answer.